Semiconductor devices such as logic and memory devices are typically fabricated by a sequence of processing steps applied to a specimen. The various features and multiple structural levels of the semiconductor devices are formed by these processing steps. For example, lithography among others is one semiconductor fabrication process that involves generating a pattern on a semiconductor wafer. Additional examples of semiconductor fabrication processes include, but are not limited to, chemical-mechanical polishing, etch, deposition, and ion implantation. Multiple semiconductor devices may be fabricated on a single semiconductor wafer and then separated into individual semiconductor devices.
Optical metrology processes are used at various steps during a semiconductor manufacturing process to detect defects on wafers to promote higher yield. Optical metrology techniques offer the potential for high throughput without the risk of sample destruction. A number of optical metrology based techniques including scatterometry and reflectometry implementations and associated analysis algorithms are commonly used to characterize critical dimensions, film thicknesses, process parameters, composition and other parameters of nanoscale structures.
As devices (e.g., logic and memory devices) move toward smaller nanometer-scale dimensions, characterization becomes more difficult. Devices incorporating complex three-dimensional geometry and materials with diverse physical properties contribute to characterization difficulty.
In response to these challenges, more complex optical tools have been developed. Measurements are performed over a large ranges of several machine parameters (e.g., wavelength, azimuth and angle of incidence, etc.), and often simultaneously. As a result, the measurement time, computation time, and the overall time to generate reliable results, including measurement recipes, increases significantly.
Existing model based metrology methods typically include a series of steps to model and then measure structure parameters. Typically, measurement data (e.g., DOE spectra) is collected from a particular metrology target. An accurate measurement model of the optical system, dispersion parameters, and geometric features is formulated. An electromagnetic (EM) solver is employed to solve the measurement model and predict measurement results. A series of simulations, analysis, and regressions are performed to refine the geometric model and determine which model parameters to float. In some examples, a library of synthetic spectra is generated. Finally, measurements are performed using the library or regression in real time with the geometric model. The EM simulation process is controlled by a number of parameters (e.g., slabbing parameters, Rigorous Coupled Wave Analysis (RCWA) parameters, discretization parameters, etc.). Simulation parameters are selected to avoid introducing excessively large errors. However, in general, there is a trade-off between computational effort and solution accuracy. In other words, an accurate solution requires much more computational effort than a less accurate solution. Currently, the computational effort required to arrive at sufficiently accurate measurement results for complex semiconductor structures is large and growing larger.
Many current systems employ a RCWA algorithm to solve the measurement model. Simulated measurement signals are computed by the RCWA engine. Measured signals are compared to the computed signals as part of a regression analysis to estimate measurement parameter values. When current systems are employed to measure complex geometric structures, three dimensional structures, and large pitch structures, a high truncation order is necessary to accurately represent the corresponding physical measurement signals. This significantly increases the required computational effort. In a further example, simulated measurement signals are integrated for multiple angles of incidence present in the optical path of the measurement system. This is commonly referred to as “NA integration.” Computational effort increases proportionally with the number of angles.
To meet the increasing computational burden, large computing clusters are required, and in some cases it is impractical to perform the necessary computations for some models. Although a lower truncation order or reduced NA integration may be employed to reduce the required computational effort, this often results in unacceptably large measurement errors.
Increasingly complicated measurement models are causing corresponding increases in computational effort. Improved model solution methods and tools are desired to arrive at sufficiently accurate measurement results with reduced computational effort.